Are you using their in-house production talent? Have they discussed pre-production with you so that you have your act together before the session starts? Being prepared in advance (arrangements, charts, instrumentation and requisite amplifers, etc) will save you a LOT of $$$ if you have all your ducks in a row ahead of time. Of course, if the place is accustomed to scamming its clients, they won't emphasize this aspect and let you run up a tidy sum in hourly rates...
Also, ask how they charge for the media (tape, CDs, hard drives, etc) that they will be tracking you to. Get references from them, preferably involving someone with a similar musical genre as yours. If you're taking a tour of the place, look around and see if the business looks as if it's being run...like a business. Is it reasonably neat and clean? Don't laugh...there's a lot of gear to maintain, even in these days of DAWs, and lack of maintenance will wreak havoc on a session. A messy room with an engineer running around like a chicken with its head cut off can be a sure sign of trouble.
Do you use a drummer? Yours or theirs? The drumkit-yours or theirs? Take your drummer with you to clear that issue up (this can be a double-edged sword.I had one guy get SO beligerent about mic'ing the drums HIS way, he was turned down). If you are bringing in your own gear, do they give you a checklist of "Do's and Dont's" to speed up the session (like, DO have extra sticks, strings, picks, cords, heads,etc, and DON'T bring in gear that you aren't familiar with just because you want to 'experiment' during the session). Remember that it is THEIR room and services, but it's YOUR money. Be clear what you expect and get it in writing. I know that I've missed a lot, but that should get you started...

As far as the actual gear is concerned, that is far less important than the actual talent involved in making your vision come true. That said, I believe that the (2) most important pieces are the mics and the monitor speakers, and in both cases their environment (room size). Do they hype the latest digital audio exasperrator or their mic collection? Are the monitor speakers a reputable brand (JBL,KRK, Yamaha, Genelec, Dynaudio,etc) or some hi-fi offbrand? Do they have more than 1 type of monitor to check the mix over a variety of systems (we call that "translation" between systems). OFTEN a mix will sound great in the control room, but then when you play the CD on your car's stereo ( or a boombox,etc), it will sound like crap. Will they let you verify the mix that way?
I gotta go, but this is some food for thought...

Most reputable studios will offer some time to talk before the first day of the session. This is a good time to ask questions. Find out how they charge, at what rate and for what. Some studios have block booking rates, some have different rates for "off peak time" some have different rates at night. .

If they seem vague or start throwing out a lot of techno babble then ask for clarification. Most studios are run as businesses and they have costs to cover and are trying to make a small profit on the recording they do. Some are trying to rip people off. Sometimes there is a fine line between doing a good job at reasonable rates and ripping someone off.

Look around the studio. Are things more or less neat and tidy or is the studio and control room a mess with half eaten sandwiches laying around and cigarette butts on the floor. Does the place look professional or like the day after a party the night before.

Ask about their mic cabinet and what they have in the way of microphones and direct boxes. If they will not tell you names and model numbers ask for them. Watch for descriptions like "all of our microphones are professional" or "we have a lot of good microphones that will be just right for your recording" neither of these statements tells you anything except they are being evasive.

Take a look around the control room and see if the equipment looks in good condition and is well maintained. If there is an inch of dust on everything then I would question how busy they are. If stuff is just laying about without being in a rack or some kind of enclosure without a patch bay to connect it all together ask yourself how long is it going to take to setup a needed piece of equipment during the sessions.

Ask what you are going to be recorded on and how they will give you the final master. If they are using ADATs do you get the tapes at the end of the session for back up or are they using the same tapes over and over. If it is hard disk do you have to purchase it before or after the session and what kind of program are they using for the recording. It does no good to have backups of your session if the program used to create them is not something that other studios would have access to. There are a lot of DAW programs out there and most of them create WAV or AIFF files that can be transported to other studios but some DAWs create very specific files that are proprietary and you do not have the program they were created on you cannot play them back which would mean you have to return to the studio that created the files.

Ask yourself if you would be comfortable working in the studio for 40 hours or more and if the general ambiance is such that you could do work and be creative in for a period of time. Sometimes color schemes and physical layout can have a major influence on your creativity so ask those questions to yourself early on.

As to rates and working arrangements. Some studios will allow you do your setup and tune your drums and guitars with out a charge some have a "drop to dash clause" meaning that the minute you set foot in the studio the clock starts and will continue to the time your last piece of equipment is taken out of the studio. Some studios will stop the clock if someone has to take a bathroom break some studios the clock is running the whole time. Some studios will spring for lunch some will charge a hospitality fee which could be a sizable amount tacked onto your bill.

Ask also about "other" charges like media costs, copying fees for the master CD or DAT, rental charges for additional equipment (some studios I have worked in have only a basic setup and every piece of extra equipment has to be rented (either from them or a rental outfit) so make sure that you have some agreement with them (a signed contract would be a very good idea) so that you know EXACTLY what is covered in the basic time fee and what are the extras.

Most studios are very good and they treat their clients the way they would like to be treated if the roles were reversed but SOME studios make it a habit of offering low hourly rates and then do a lot of add ons that can send their low hourly rate into orbit.

Best of luck. Go into this arrangement with an open mind and ask lots of questions. You cannot be too careful in selecting someone to do your recording.